The fatal flaw is that the adversary can shoot down the orbital segment before it is deployed.
It will result in a political crisis and some retaliation, but ultimately nobody will start a preemptive nuclear war because their shiny toy was destroyed before it could be operational, or even a preemptive large scale war, since there would be no political capital to be spent over some satellites being destroyed, with no casualties.
The idea that shooting down satellites is a line that shouldn't be crossed mainly exists because there is no precedent, once it happens, life will go on, as it always does.